Global Attractors For A Weighted P(X)-laplacian Evolution Equation With Boundary Degeneracy

In this paper, the longer-time behavior for a class of weighted p(x)-Laplacian evolution equation will be considered in a bounded domain, where the nonnegative diffusion coefficient ω is allowed to vanish on boundary, the nonlinearity f satisfies a polynomial growth of arbitrary order and g, u0∈L2(Ω). Firstly, the global existence and uniqueness of weak solution will be shown in variable exponent spaces using approximating degenerate problems by non-degenerate ones; Secondly, we prove the existence of absorbing sets in Lq(x)(q(x)≥2) and W/1,p(x)(ω,Ω),and obtain the the existence of global attract or in L2(Ω) using the method of uniform compactness; At last, the existence of global attract ors in Lq(x)(Ω) and W0/1,q(x)(ω,Ω) are established by the method of asymptotic a prior estimates and the notion of norrn-to-weak continuous semigroup,respectively.